Three uniform rods, each of length 21 ( = 1m) and mass M = 8 kg are rigidly joined at their ends to form a triangular framework. Find the moment of inertia of the framework about an axis passing through the midpoints of two of its sides?

Explanation

To find the moment of inertia of the triangular framework formed by three uniform rods about an axis passing through the midpoints of two of its sides, we can follow these steps:

### Step 1: Understand the Configuration
We have three uniform rods, each of length \( L = 1 \, \text{m} \) (since \( 2L = 1 \, \text{m} \) implies \( L = 0.5 \, \text{m} \)) and mass \( M = 8 \, \text{kg} \). These rods are arranged to form an equilateral triangle.

### Step 2: Identify the Axis of Rotation
The axis of rotation passes through the midpoints of two sides of the triangle. Let's denote the vertices of the triangle as A, B, and C. The midpoints of sides AB and AC will be denoted as D and E, respectively.

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